Abstract:  A well-known result in the Bayesian inventory management research is: if lost sales are not observed, the Bayesian optimal inventory level is larger than the myopic inventory level. The underlying reason behind the fact is that the decision maker needs to stock more to learn about the demand distribution. These researches are based on the assumption that the decision maker is risk neutral. However, in reality, different decision makers often have different degree of risk aversion. In this paper, a multi-period newsvendor problem with risk aversion and partially observed demand is considered. The decision maker uses the Bayesian rule to update the information of the demand distribution, and the utility is characterized by the sum of the intraperiod utility functions which satisfy the additive independence axiom. Our research, by using the interesting concept of unnormalized probability, shows that as the decision maker is risk averse and the utility function is the negative exponential function with a constant coefficient of absolute risk aversion, the Bayesian optimal inventory level is also larger than the myopic inventory level. The unnormalized probability greatly simplifies the dynamic programming equation and facilitates the technical proof of the result.

Key words: Bayesian information updating, risk averse, inventory, unnormalized probability